Question: Given $ m \angle LOM = 6x + 9$, $ m \angle MON = 8x + 40$, and $ m \angle LON = 63$, find $m\angle MON$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {6x + 9} + {8x + 40} = {63}$ Combine like terms: $ 14x + 49 = 63$ Subtract $49$ from both sides: $ 14x = 14$ Divide both sides by $14$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 8({1}) + 40$ Simplify: $ {m\angle MON = 8 + 40}$ So ${m\angle MON = 48}$.